Multiplication of vectors by scalars
Motion in a plane · Physics
Projectile launcher
Interactive 3DFire the cannon and watch the ball follow its true trajectory — range, apex and flight time update live.
Controls
Drag the sliders or type a value — the simulation updates live.
m/s
5m/s50m/s
°
10°80°
Study notes
A ball is kicked at 20 m/s at 45° to the horizontal (g = 9.81 m/s²). Horizontal component: 20·cos45° ≈ 14.14 m/s; vertical: 20·sin45° ≈ 14.14 m/s. Time of flight = 2×14.14/9.81 ≈ 2.88 s. Range = 14.14×2.88 ≈ 40.8 m. Maximum height = 14.14²/(2×9.81) ≈ 10.2 m. 45° gives the maximum range for a given speed — try other angles in the simulator above.